A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations

In this paper, reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order Fredholm-Volterra integrodifferential equations. The analytical solution was calculated in the form of convergent series in the space W25[a,b] with easily computable components. In the proposed method, the n-term approximation is obtained and is proved to converge to the analytical solution. Meanwhile, the error of the approximate solution is monotone decreasing in the sense of the norm of W25[a,b]. The proposed technique is applied to several examples to illustrate the accuracy, efficiency, and applicability of the method.